\(\left(\dfrac{3x}{2}-1\right)^2-\dfrac{x}{2}\cdot\left(\dfrac{5x}{2}-2\right)\le0\) (1)
\(\Leftrightarrow\dfrac{9x^2}{4}-\dfrac{6x}{2}+1-\dfrac{x}{2}\cdot\dfrac{5x-4}{2}\le0\)
\(\Leftrightarrow\dfrac{9x^2}{4}-3x+1-\dfrac{x\left(5x-4\right)}{4}\le0\)
\(\Leftrightarrow\dfrac{9x^2}{4}-3x+1-\dfrac{5x^2-4x}{4}\le0\)
\(\Leftrightarrow9x^2-12x+4-\left(5x^2-4x\right)\le0\)
\(\Leftrightarrow9x^2-12x+4-5x^2+4x\le0\)
\(\Leftrightarrow4x^2-8x+4\le0\)
\(\Leftrightarrow x^2-2x+1\le0\)
\(\Leftrightarrow\left(x-1\right)^2\le0\)
\(\Leftrightarrow\left(x-1\right)^2=0\)
\(\Leftrightarrow x=1\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{1\right\}\)
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